Communication complexity in number-conserving and monotone cellular automata

Authors:
E. Goles;A. Moreira;I. Rapaport
Affiliations:
Universidad Adolfo Ibáñez, Av. Diagonal Las Torres 2640, Peñalolén, Santiago, Chile and Institute for Complex Systems (ISCV), Subida Artillería 470, Valparaíso, Chile;Departamento de Informática and Centro Tecnológico de Valparaíso (CCTVal), Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile and Institute fo ...;DIM, CMM (UMI 2807 CNRS), Universidad de Chile, Av. Blanco Encalada 2120, Santiago, Chile
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

One third of the elementary cellular automata (CAs) are either number-conserving (NCCAs) or monotone (increasing or decreasing). In this paper we prove that, for all of them, we can find linear or constant communication protocols for the prediction problem. In other words, we are able to give a succinct description for their dynamics. This is not necessarily true for general NCCAs. In fact, we also show how to explicitly construct, from any CA, a new NCCA which preserves the original communication complexity.